Richard Kaye’s Minesweeper NP-Completeness Pages
Web page and associated articles that introduce the notion of NP-completeness and show that “Minesweeper is NP-complete.” Minsweeper was the focus in 2000 for a series of popular lectures by Ian Stewart on NP-completeness connected with the Clay Mathematics Institute. Includes a link to a talk about the result and a followup article, but unfortunately not the original Mathematical Intelligencer article.

How To Explain Zero-Knowledge Protocols To Your Children
Bedtime story that illustrates the notion of “simulator” used in cryptographic zero-knowledge proofs. Introduces the exceedingly clever Mick Ali as the descendant of Ali Baba. Beware: most people I try this on ask me “but why didn’t Mick Ali just walk in one side of the cave and then walk out the other?” Replying “because that’s how the math we are trying to allegorize actually works” is not so satisfying.

Kid Krypto by Neal Koblitz. Article that discusses strategies for teaching “kid cryptography” to high school (and younger) students. Includes “Kid RSA,” an averaging protocol secure against honest but curious kids, and “perfect codes.” Also includes experience with trying out these ideas with actual high school students.

Computer Science Unplugged by Tim Bell, Ian H. Witten and Mike Fellows. A number of games designed to teach a variety of mostly TCS concepts.

Theory of Computation: A Scientific Perspective by Oded Goldreich and Avi Wigderson – provides an assessment of the Theory of Computing (TOC) as a fundamental scientific discipline. The focus is on the important scientific role of TOC, and on its great achievements, productivity and impact (both scientific and technological) so far. Also includes brief layman-level introductions to four concrete topics.

The Computational Worldview and the Sciences: a Report on Two Workshops, by Sanjeev Arora, Avrim Blum, Leonard Schulman, Alistair Sinclair, and Vijay Vazirani (2007). Discusses many connections between theoretical computer science and game theory and economics, quantum information and computation, statistical physics, neuroscience, systems biology and genetics, synthetic biology, control theory, nanotechnology, astrophysics, social sciences, and mathematics.

An Introduction to Bioinformatics Algorithms by Jones and Pevzner. A good introduction to how the study of algorithms has shaped the course of Biology in recent decades. Also has good biopics of some of the leading figures from TCS in bioinformatics, including Karp, Myers, and Haussler.

Randomness and Computation by Oded Goldreich
Following a general introduction to the two notions and their possible relation, the essey contains brief accounts of pseudorandomness and probabilistic proof systems and every shorter accounts of cryptography and sub-linear time algorithms.

Popular books (not aimed at students)

Computers Ltd: What they really can’t do by David Harel. This is a beautiful, well-written and enjoyable book. It presents with meticulous clarity the fundamental results of computability and complexity theory to a non-mathematical audience, and briefly surveys novel models of computation such as quantum computing and molecular computing. Harel also explains how the computational intractability of some problems can be put to good use in fields like public-key cryptography. There should be more books like this one!

Algorithmics: The Spirit of Computing by David Harel and Yishai Feldman. From the Amazon page: “First published in 1987, explains the basic ideas of algorithms, their structures, and how they manipulate data in computer programs. Of interest to programmers, systems analysts and designers, and software engineers, but the technical level is low enough to be accessible to readers with almost no mathematics or computer background.” Makes it sound like a version of _What Is Mathematics?_ for TCS.

Ideas from Other Fields (to inspire us)

The Clay Mathematics Institute sponsored a series of popular lectures on NP-completeness in 2000. They also provided support for the PCMI/IAS program on Computational Complexity that year. They also do outreach and education concerning pure and applied mathematical topics.